I need to find angle M

m<AIR = 90 deg

Step-by-step explanation:

I assume the problem contains an error, and that AR is a diameter, not AC.

Look at the diameter of the circle, AR. It passes through the center of the circle, C. You can think of the two radii of the circle, CR and CA, as sides of angle RCA. Since AR is a diameter, and AR is a segment which is part of line AR, rays CR and CA are sides of an angle that lie on a line. That makes the measure of angle RCA 180 deg. Angle RCA is a central angle of circle C since its vertex is the center of the circle.

Angle AIR is an inscribed angle in circle C since its vertex is on the circle itself. If an inscribed angle and a central angle intercept the circle at the same two points, then the measure of the inscribed angle is half the measure of the central angle.

m<AIR = (1/2)m<RCA = (1/2) * 180 = 90

m<AIR = 90 deg

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step-by-step explanation:

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